Stellar Physics – Gaps in the Spectrum

The following is an excerpt from my e-book “Introduction to Stars: Spectra, Formation, Evolution, Collapse” available here for Kindle.

When you look at the spectrum of the heat radiation coming from glowing metal, you will find a continuous spectrum, that is, one that does not have any gaps. You would expect to see the same when looking at light coming from a star. However, there is one significant difference: all stellar spectra have gaps (dark lines) in them. In other words: photons of certain wavelengths seem to be either completely missing or at least arriving in much smaller numbers. Aside from these gaps though, the spectrum is just what you’d expect to see when looking at a heat radiator. So what’s going on here? What can we learn from these gaps?

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Spectrum of the Sun. Note the pronounced gaps.

To understand this, we need to delve into atomic physics, or to be more specific, look at how atoms interact with photons. Every atom can only absorb or emit photons of specific wavelengths. Hydrogen atoms for example will absorb photons having the wavelength 4102 A, but do not care about photons having a wavelength 4000 A or 4200 A. Those photons just pass through it without any interaction taking place. Sodium atoms prefer photons with a wavelength 5890 A, when a photon of wavelength 5800 A or 6000 A comes by, the sodium atom is not at all impressed. This is a property you need to keep in mind: every atom absorbs or emits only photons of specific wavelengths.

Suppose a 4102 A photon hits a hydrogen atom. The atom will then absorb the photon, which in crude terms means that the photon “vanishes” and its energy is transferred to one of the atom’s electrons. The electron is now at a higher energy level. However, this state is unstable. After a very short time, the electron returns to a lower energy level and during this process a new photon appears, again having the wavelength 4102 A. So it seems like nothing was gained or lost. Photon comes in, vanishes, electron gains energy, electron loses energy again, photon of same wavelength appears. This seems pointless, why bother mentioning it? Here’s why. The photon that is created when the electron returns to the lower energy level is emitted in a random direction and not the direction the initial photon came from. This is an important point! We can understand the gaps in a spectrum by pondering the consequences of this fact.

Suppose both of us observe a certain heat source. The light from this source reaches me directly while you see the light through a cloud of hydrogen. Both of us are equipped with a device that generates the spectrum of the incoming light. Comparing the resulting spectra, we would see that they are for the most part the same. This is because most photons pass through the hydrogen cloud without any interaction. Consider for example photons of wavelength 5000 A. Hydrogen does not absorb or emit photons of this wavelength, so we will both record the same light intensity at 5000 A. But what about the photons with a 4102 A wavelength?

Imagine a directed stream of these particular photons passing through the hydrogen cloud. As they get absorbed and re-emitted, they get thrown into random directions. Only those photons which do not encounter a hydrogen atom and those which randomly get thrown in your direction will reach your position. Unless the hydrogen cloud is very thin and has a low density, that’s only a very small part of the initial stream. Hence, your spectrum will show a pronounced gap, a line of low light intensity, at λ = 4102 A while in my spectrum no such gap exists.

What if it were a sodium instead of hydrogen cloud? Using the same logic, we can see that now your spectrum should show a gap at λ = 5890 A since this is the characteristic wavelength at which sodium atoms absorb and emit photons. And if it were a mix of hydrogen and sodium, you’d see two dark lines, one at λ = 4102 A due to the presence of hydrogen atoms and another one at λ = 5890 A due to the sodium atoms. Of course, and here comes the fun part, we can reverse this logic. If you record a spectrum and you see gaps at λ = 4102 A and λ = 5890 A, you know for sure that the light must have passed through a gas that contains hydrogen and sodium. So the seemingly unremarkable gaps in a spectrum are actually a neat way of determining what elements sit in a star’s atmosphere! This means that by just looking at a star’s spectrum we can not only determine its temperature, but also its chemical composition at the surface. Here are the results for the Sun:

– Hydrogen 73.5 %

– Helium 24.9 %

– Oxygen 0.8 %

– Carbon 0.3 %

– Iron 0.2 %

– Neon 0.1 %

There are also traces (< 0.1 %) of nitrogen, silicon, magnesium and sulfur. This composition is quite typical for other stars and the universe as a whole: lots of hydrogen (the lightest element), a bit of helium (the second lightest element) and very little of everything else. Mathematical models suggest that even though the interior composition changes significantly over the life time of a star (the reason being fusion, in particular the transformation of hydrogen into helium), its surface composition remains relatively constant in this time.

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